Math Questions

I took the daily performance of my fund and doubled the daily gain or loss per day. I then applied the same statistical metrics to these doubled figures as I do for the original values. Logically, I would have thought that the metrics also would have doubled. For example, I would have expected a figure of .084% to go .168%. However, what I found was that the figure went to .277%. This "exageration" occurred throughout all of the metrics I applied. In addition, I found an even greater "exageration" when I tripled the numbers. I would expect this condition would grow more extreme as I continue multiplying the original figures...

One series of studies I did was to find out what were the important factors in consistency. I did tests on size of expectation, % wins, profit factor, number of trades within a timeframe, and the effect of dispersion of trades (std. deviation) has on the results. For instance, here's a run for a daytrader that does 10 trades a day with 70% wins and makes $500 on each win and loses $500 on each loss. As you can see this is quite profitable at the 50% level (the average over time). However you can also see that after the 80% level the trader actually loses money. So for a daytrader with these numbers they only have a 80% chance of achieving their goal of consistent profitability on a daily basis. If that level of confidence is ok, then they have a example to use going forward.

Now what happens if that daytrader decides he wants 95% level of confidence so that he'll accpect one losing day per month. What changes would he make? If he doubles his expectation does that help? As you can see from this run, he still only has about 80% confidence level with double the expectancy on each trade.

As requested, I have attached the spreadsheet example to this post to include all formulas. An example of what specifically confuses me is the relationship between cells D2, K2 and R2, however this trend can be observed to occur throughout almost all of the metrics.

One series of studies I did was to find out what were the important factors in consistency. I did tests on size of expectation, % wins, profit factor, number of trades within a timeframe, and the effect of dispersion of trades (std. deviation) has on the results. For instance, here's a run for a daytrader that does 10 trades a day with 70% wins and makes $500 on each win and loses $500 on each loss. As you can see this is quite profitable at the 50% level (the average over time). However you can also see that after the 80% level the trader actually loses money. So for a daytrader with these numbers they only have a 80% chance of achieving their goal of consistent profitability on a daily basis. If that level of confidence is ok, then they have a example to use going forward.

Now what happens if that daytrader decides he wants 95% level of confidence so that he'll accpect one losing day per month. What changes would he make? If he doubles his expectation does that help? As you can see from this run, he still only has about 80% confidence level with double the expectancy on each trade.

Path dependency or path asymmetry if you like.
By doubling incremental values of steps in a random (even deterministic) trajectory, the new trajectory measurements at longer lengths will not scale at double the underlying termination measure.

You'll notice that the overall % return of "Actual" is 0.05069%
and the % return of "2x Actual" is 0.101386% or, 2 times Actual's return. That works because they both use the same starting value and every day's $ value return was doubled for "2x Actual".
What you did in D2 and K2 is not 2x because there are many % returns during the time period that are not 2x because of the reason given above by dtrader. For example, J20's 3.87% is not 2x C20's 1.86% because Actual was using with 214,268.07 and 2x Actual is using 205,705.25.
If you want K2 to be 2x D2 you'd want to double the percentage returns of each day, not double the dollar amounts.

I see your point, Monstimal. I can't believe I didn't catch that by myself but I thank you for pointing it out. Pretty obvious to me now.

Thanks again.

Quote from monstimal:

You'll notice that the overall % return of "Actual" is 0.05069%
and the % return of "2x Actual" is 0.101386% or, 2 times Actual's return. That works because they both use the same starting value and every day's $ value return was doubled for "2x Actual".
What you did in D2 and K2 is not 2x because there are many % returns during the time period that are not 2x because of the reason given above by dtrader. For example, J20's 3.87% is not 2x C20's 1.86% because Actual was using with 214,268.07 and 2x Actual is using 205,705.25.
If you want K2 to be 2x D2 you'd want to double the percentage returns of each day, not double the dollar amounts.